#1
Which of the following is a quadratic polynomial?
4x^2 - 5x + 1
ExplanationQuadratic polynomials have a degree of 2.
#2
What is the degree of the polynomial 3x^4 - 2x^2 + 5?
4
ExplanationThe degree is the highest power of x, which is 4 in this case.
#3
What is the degree of the polynomial 6x^4 + 3x^3 - 2x^2 + 8?
4
ExplanationThe degree is the highest power of x, which is 4 in this case.
#4
What is the solution to the equation x^2 - 9 = 0?
x = ±3
ExplanationSolving the quadratic equation gives the values of x.
#5
What is the factorization of the expression 4x^2 - 25y^2?
(2x - 5y)(2x + 5y)
ExplanationThe expression is factored using the difference of squares formula.
#6
Which method is used to find the roots of a quadratic equation?
All of the above
ExplanationQuadratic equations can be solved using factoring, quadratic formula, and completing the square.
#7
Factorize the quadratic expression: 2x^2 - 8x + 6
(2x - 3)(x - 2)
ExplanationFactorizing the quadratic expression yields its factored form.
#8
If one root of the quadratic equation ax^2 + bx + c = 0 is 3, what is the other root?
-b/a
ExplanationThe sum of roots is -b/a, so the other root is -b/a - 3.
#9
What is the sum of the roots of the quadratic equation 2x^2 - 5x + 3 = 0?
5/2
ExplanationThe sum of roots is -b/a, so in this case, it is 5/2.
#10
Solve the equation x^2 - 4 = 0.
x = ±2
ExplanationSolving the quadratic equation gives the values of x.
#11
Which method is used to factorize a quadratic trinomial in the form ax^2 + bx + c when 'a' is not equal to 1?
Factoring by grouping
ExplanationGrouping similar terms is used to factorize such trinomials.
#12
What is the remainder when dividing 4x^3 - 9x^2 + 5x - 7 by (x - 2)?
-3
ExplanationThe remainder is found by substituting 2 into the polynomial.
#13
Which method is used to factorize a cubic polynomial?
Long division
ExplanationLong division is commonly used to factorize cubic polynomials.
#14
What is the product of the roots of the quadratic equation 4x^2 - 7x + 2 = 0?
1/2
ExplanationThe product of roots is c/a, so in this case, it is 1/2.
#15
Factorize the following expression: x^3 - 8
(x - 2)(x^2 + 2x + 4)
ExplanationThe expression is factored using the difference of cubes formula.
#16
What is the remainder when dividing the polynomial 3x^4 - 7x^3 + 5x^2 - 9x + 2 by (x - 1)?
4
ExplanationThe remainder is found by substituting 1 into the polynomial.
#17
Find the value of 'k' for which x + k is a factor of the polynomial 2x^2 - 5x - 3.
-1
ExplanationSetting x + k as a factor, and finding its root gives k.